for n = 1 LHS = 10
Assume true for n = k where k is an integer i.e \\ 5^k +6^k - 1 = 10M
for n = k+1 (I'll be skipping most of the algebra)
\\ 5^{k+1} + 6^{k+1} - 1 = \\ \ 5^{k+1} + 6(10M + 1 - 5^k) -1 = \\ 60M + 5 - 5^k
now 5 - 5^k is divisible by 10 since 5^k will always have the last...